Statistical Discrimination and A rmative Action in …fede/wp/discrimination.pdfStatistical...

Statistical Discrimination and Affirmative Actionin the Lab∗

Ahrash DianatUniversity of Essex

[email protected]

Federico EcheniqueCaltech

[email protected]

Leeat YarivPrinceton [email protected]

May 11, 2020

Abstract

We present results from laboratory experiments studying statistical discrimination andaffirmative action. We induce statistical discrimination in simple labor-market inter-actions between firms and workers. We then introduce affirmative-action policies thatvary in the size and duration of a subsidy that firms receive for hiring discriminated-against workers. These different affirmative-action policies have nearly the same effect,and practically eliminate discriminatory hiring practices. However, once lifted, fewpositive effects remain and discrimination reverts to its initial levels. One exception islengthy affirmative-action policies, which exhibit somewhat longer-lived effects. Stick-iness of beliefs, which we elicit, helps explain the observed outcomes.

JEL Classifications: J71, D04, C91Keywords: Statistical Discrimination, Affirmative Action, Experiments

∗We thank Richard Sander for very helpful comments. Echenique gratefully acknowledges the supportof NSF grants SES-1558757 and CNS-1518941. Yariv gratefully acknowledges the support of NSF grantSES-1629613. Prior to conducting the study, the authors obtained ethical approval from the Committee forthe Protection of Human Subjects at the California Institute of Technology.

1 Introduction

Affirmative-action policies have had a tumultuous history since their introduction over 50

years ago in the U.S.1 Intended to alleviate inequality in employment and pay, increase

access to education, and promote diversity, they have been a subject of legal and political

controversy. In their various forms, they are often set as a temporary “nudge”, put in place

for a limited duration. For instance, in 2003, the Supreme Court ruled the use of race for

affirmative action in school admissions as constitutional (Grutter v. Bollinger). Justice

Sandra Day O’Connor famously stated that:

“We expect that 25 years from now, the use of racial preferences will no longer

be necessary to further the interest [in student-body diversity] approved today.”

In this paper, we focus on statistical discrimination, where the source of unequal treatment

is a correct statistical evaluation of past performance of different groups of individuals,

rather than differential tastes. Our goal is to assess experimentally the efficacy of several

affirmative-action policies for generating equal treatment while in place and, especially, after

they are lifted.

Our results are threefold. The first is methodological: we are able to induce statistical

discrimination in the laboratory, where workers from a disadvantaged group are discrim-

inated against despite the absence of any exogenous differences between them. We con-

sider affirmative-action policies that seek to reverse the induced discriminatory attitudes

by rewarding firms for hiring disadvantaged workers. Rewards are of varying amounts and

duration. Our second finding is that such policies, while in place, generally succeed in elim-

inating discrimination and lead to similar hiring rates of all workers. However, our third

and arguably most important finding is that when affirmative-action policies are removed,

statistical discrimination rears its head and returns to its original levels. Furthermore, our

1The term “affirmative action” was introduced by President John F. Kennedy in an executive order in 1961as a method for redressing discrimination that had persisted in spite of civil rights laws and constitutionalguarantees. It was further developed and enforced under President Lyndon B. Johnson.

1

elicitation of beliefs suggests one mechanism for the behaviour we observe—beliefs change

slower than actions. The main message of the paper therefore implies more limited optimism

than Justice O’Connor’s statement—while affirmative-action policies are effective tools for

combating inequality while in place, their impact is short-lived. Once lifted, behaviour re-

verts back to the unequal treatment that affirmative action was designed to undo.

Arrow (1998) argues that taste-based discrimination cannot explain unequal treatment

of workers in the market since there would be arbitrage opportunities that would eventually

drive out discriminating employers. Arrow concludes that statistical discrimination is the

leading hypothesis for explaining the prevalence of discrimination in market settings. In

reality, taste-based discrimination might still be present despite competitive pressures. This

possibility makes field data particularly difficult to work with, as both types of discrimination

could impact observed outcomes. The experimental lab allows us to isolate one channel.

Our experimental design is a particularly simple operationalisation of the statistical dis-

crimination model suggested by Kenneth Arrow (1971; 1973). In Arrow’s model, statistical

discrimination is the manifestation of a coordination failure.2 Simplified, the game under-

lying Arrow’s analysis can be described as follows. Agents interact in worker-firm pairs. A

worker may invest in a firm-specific skill, but this investment is worthwhile only if she is

hired. For the firm, hiring a worker is desirable only if the worker has invested in acquiring

the skill. However, workers and firms do not know each other’s choices when making their

own.3 The resulting game has two Pareto-ranked pure equilibria. In one, the worker invests

and the firm hires. In the other, the worker does not invest and the firm does not hire.

In our experiments, workers are of two types: green and purple. Colours are a metaphor

for group association, and substitute for observable characteristics of real-world workers (e.g.,

gender, race). Colours can serve as a coordination device, with different equilibria being fol-

2Arrow’s model assumes a perfectly symmetric situation and generates differences among groups endoge-nously. Phelps (1972a) also proposes statistical discrimination as an explanation for observed discriminatoryoutcomes, but his explanation requires the existence of genuine exogenous differences between groups.

3There are, of course, examples of human capital investments that are unobservable by firms. The modelis a simplification of reality and our assumptions are meant to capture that worker quality is only imperfectlyobserved in real-life labor markets.

2

lowed when different types of workers are involved. Importantly, worker colour is observable,

both in our experiments and their real-world analogues. We term outcomes in which agents

play different equilibria, depending on the colour of the worker, as discriminatory.

In each of our sessions, experimental workers and firms are randomly matched, and play

the game multiple times. All participants observe a moving average of historical play—worker

investment levels and firm hiring rates—pertaining to both green and purple workers. The

aggregate public history of play allows us to capture discriminatory path-dependent outcomes

observed in the real world. It also provides a channel for hysteresis that allows us to induce

discrimination in the lab.

Our sessions are comprised of four stages. First, our participants play a version of the

game in which purple workers are less productive than green workers, i.e. have higher costs

of investment. This first stage of the game “seeds” the discriminatory outcome.

In the second stage, we equalise the costs of investment across workers so that there are

no material differences between the two worker groups. The history of play is enough to

generate discriminatory outcomes: we find that participants coordinate on the inefficient

equilibrium (no-investment and no-hiring) when the participating worker is purple. Indeed,

in almost all sessions, firms hire purple workers at significantly lower rates than green workers,

as they correctly anticipate that purple workers will invest at lower rates. Conversely, purple

workers invest less than green workers as they correctly anticipate that they will not be

hired as often. These observations illustrate two points. First, our method of inducing

discrimination is effective. Second, when we equalise conditions, discrimination remains.

In particular, equalisation in and of itself is insufficient to redress discrimination due to a

historically unequal environment.

The third stage introduces affirmative action. Namely, firms are rewarded for hiring

purple workers. We vary the magnitude of the reward and the duration of affirmative action

across treatments. Despite a salient public history of inefficient outcomes associated with

purple workers, we now see firms more willing to hire purple workers. In turn, purple

3

(a) Workers’ investment decisions (b) Firms’ hiring decisions

Figure 1: Behavior across experimental stages in benchmark treatment

workers invest at greater rates. Across our treatments, while affirmative action is in place,

discrimination essentially goes away.

Finally, in the last stage, we lift the affirmative-action policy. Thus, the last stage is

identical to the second stage, in which the environment is perfectly symmetric across worker

types. In all our treatments, participants’ play reverts back to the discriminatory profile

we observed in the second stage of our experiment: purple workers invest less often than

green workers, and are hired less often. In other words, the effects of affirmative action are

short-lived. One exception is the treatment in which affirmative action was imposed for a

relatively long duration, for double the number of periods of each of the other stages. In

that case, some improvement is seen even after the policy is lifted, but outcomes are still

significantly different from those implied by an equal treatment of workers.

Figure 1 illustrates our main findings through our benchmark treatment, entailing a

moderate affirmative-action subsidy for a duration that equals the duration of our other

experimental stages. It shows investment and hiring rates for the different stages of our

experiment, using green and purple colours to distinguish matches. The figure illustrates the

findings described above: the baseline stage exhibits statistical discrimination; affirmative

action largely equalises hiring and investment rates between green and purple workers; and

the removal of affirmative action sees participants reverting back to statistical discrimination.

4

In one of our treatments, the subsidy for hiring a purple worker is so high that it is

a dominant strategy for firms to hire, and therefore a best response for purple workers to

invest. This treatment exactly reverses the situation in the seed stage, where it is dominant

for purple workers not to invest. Even in this treatment, where we mirror the incentives

provided in the seed stage, affirmative action does not have lasting effects. We view this

result as particularly telling. Naturally, it is difficult to say when an experimental affirmative-

action policy comes close to capturing the mechanisms behind a real-world one. But a policy

that is the exact mirror image of the “seed” conditions that induced discrimination to begin

with seems like a natural candidate for undoing discrimination. We find, however, that

discrimination persists.

Why are the effects of affirmative action so short-lived? The patterns of participants’

beliefs provide some insights. Throughout our experiments, we elicit workers’ beliefs regard-

ing their probabilities of being hired, as well as firms’ beliefs regarding the probabilities that

the workers they encounter had invested. In our experiments, firms’ decisions to hire pur-

ple workers are consistent with their reported beliefs about whether workers had invested.

Affirmative-action policies change (temporarily) the decision to hire purple workers, but

firms’ beliefs do not change significantly—beliefs are sticky. These beliefs do not change

substantially when affirmative-action policies are introduced or removed. Their level is such

that hiring is optimal when subsidies are present, but not when they vanish. As firms appear

to be best responding to their beliefs and the incentives they face, this stickiness in firms’

expectations accounts for the quickly-fading impacts of affirmative action.

To summarise, with a growing desire to equalise the playing field across the market, our

results suggest that affirmative-action policies should be thought through carefully. In their

frequent forms, to be effective, they need to be both substantial in magnitude and long-lived.

5

2 Related Literature

Arrow (1998) argues that taste-based discrimination cannot explain unequal treatment of

workers in the market since there would be arbitrage opportunities that would eventually

drive out discriminating employers. Arrow concludes that statistical discrimination is the

leading hypothesis for explaining the prevalence of discrimination in market settings.

Statistical discrimination is consistent with a rich set of observations in the field. For

instance, Ewens, Tomlin, and Wang (2014) identify statistical discrimination in the US rental

market over race by analysing renters’ responses to applications from white-sounding and

African American-sounding names in various neighbourhoods. Glover, Pallais, and Pariente

(2017) consider interactions between managers and workers in grocery stores and find that

more biased managers are associated with lower performance of minority workers, a pattern

similar to that we induce in our seed stage.4

Coate and Loury (1993) provide a theoretical investigation of statistical discrimination

and affirmative action. They raise the possibility that discrimination may persist after a

period of affirmative action. Some of the basic ideas in their theoretical model are present

in our design: interactions are bilateral, between workers and firms. Workers can invest, but

an informative signal of their decision is available to the firms. Workers’ incentives to invest

are, in fact, channeled through the informative signal: greater investment is associated with

“better” signals, and higher likelihood of being hired. Our design, in contrast, is based on a

pure coordination game. Workers want to invest even if they are guaranteed to be hired: in

fact, workers’ incentives to invest are maximised then.

There are several studies that bring the Coate and Loury (1993) model to the lab. Ander-

son and Haupert (1999) and Fryer, Goeree, and Holt (2005) report on classroom experiments

that capture the main forces of Coate and Loury (1993). The design of our seeding stage is

4Bohren, Imas, and Rosenberg (2018) run a field experiment using a large online platform where userspost content that is evaluated by others on the platform. They consider the assessment of posts exogenouslyvaried by gender and history on the platform and find evidence for biased beliefs, as induced in our seedingstage, driving discriminatory attitudes.

6

inspired by these, with two important distinctions. First, we do not allow (explicit) random

signals on workers’ investment decisions. Second, workers’ incentives to invest respond to

whether they are hired or not.

Kidd, Carlin, and Pot (2008) seek to replicate some of the details in the Coate and Loury

model. In particular, their design, unlike ours, relies on an informative signal of whether a

worker has invested, and much of the analysis tests the comparative-statics results of Coate

and Loury (1993). In this setting, workers over-invest. The Kidd, Carlin, and Pot (2008)

design is one-sided: experimental participants play the role of workers, while firms’ choices

are computerised. In our study, firms’ choices are an important object for analysis, and

their evolving beliefs, which we elicit, provide hints as to the source of the limited long-run

efficacy of affirmative action we observe. Feltovich, Gangadharan, and Kidd (2013) use a

similar design to that used by Kidd, Carlin, and Pot (2008), but focus on outcomes following

the removal of an affirmative-action policy. They find that workers invest significantly more

after affirmative action is removed than when it is in place. In their design, since the

incentives to invest operate through their effects on the informative signal, workers who

know they will be hired do not have strong incentives to invest. Thus, affirmative action

suppresses investment. Our experiment has the opposite property, and we see that workers

invest more when the affirmative-action policy is in place.5

Outside of the Coate and Loury (1993) setting, various studies have looked at affirmative-

action policies in the lab. For example, in the context of gender discrimination, Niederle,

Segal, and Vesterlund (2013) illustrate the effectiveness of affirmative-action policies in in-

ducing women to compete. In contrast, Bracha, Cohen, and Conell-Price (2019) illustrate

the potential harmful effects of affirmative action through its production of stereotype threat,

whereby women are primed with negative stereotypes. Anderson, Fryer, and Holt (2006)

present a survey of experiments in psychology and economics dealing with discrimination.

5de Haan, Offerman, and Sloof (2017) study experimentally the impacts of of competition on statisticaldiscrimination. They show that, in the setting of Coate and Loury (1993), competition allows statisticaldiscrimination to emerge more easily and forcefully.

7

There is important work using field data that suggests potential shortcomings of affir-

mative action. Sander (2004) illustrates several negative impacts on African-American law

students in the US. Sander and Taylor (2012) provide a comprehensive account of the im-

pacts of affirmative-action policies on racial equality in US higher education. They suggest

that even while in place, affirmative-action policies may have had detrimental effects on

minority students.6

To conclude, we believe there are several features of our design whose combination is

absent from most of the literature on affirmative action. First, we generate discrimination

in the lab, rather than relying on participants’ existing prejudices that may vary in strength

and difficult to control for. Second, we allow both workers and firms to act strategically and

elicit all participants’ beliefs throughout the evolution of our experimental sessions. Beliefs

are challenging to elicit in the field and provide insights into the mechanisms driving the

successes and limitations of affirmative action. Last, we consider the impacts of affirmative

action not only when it is in place, but also after it is lifted.

Methodologically, our technique for seeding discrimination relies on the presence of

hysteresis—equilibrium selection at the start of the experiment affects selection later on.

Outside the context of discrimination, Brandts and Cooper (2006) and Romero (2015) illus-

trate the presence of hysteresis in standard coordination games in which payoff parameters

are changed over time.

3 Experimental Design

We start with an overview of the basic statistical-discrimination model guiding our design

and its motivations. We then set forth a detailed description of our experimental protocol.

6Krueger, Rothstein, and Turner (2006) assess empirically Justice O’Connor’s prediction that affirmativeaction would not be needed 25 years after the Grutter v. Bollinger ruling and find limited support for it.

8

3.1 Statistical Discrimination

There are two leading theories of discrimination: taste-based (Becker, 1957) and statistical

(Phelps, 1972b; Arrow, 1973). Taste-based discrimination attributes discriminatory decisions

to an inherent preference for agents of certain groups over others. Statistical discrimination

refers to the idea that, in the absence of direct information about a certain aspect of abil-

ity, a decision-maker would substitute group averages or variances corresponding to the

individual’s demographics (e.g., gender or race). It is challenging to rule out empirically

that discrimination is taste-based, but in the lab one can ensure that there is no inherent

preference for one group over another.7

Following Arrow (1971), we focus on statistical discrimination in the labor market, where

employers use observable traits to make hiring decisions. Statistical discrimination is not

based on an inherent preference for hiring people of, say, a particular race or gender, but

instead on a real or perceived correlation between an observable trait and unobservable

productivity, or some unobservable aspect that informs the quality of a hire.

We consider statistical discrimination as a self-fulfilling equilibrium phenomenon. The

model guiding our design is a stylised version of the model proposed by Arrow (1971)8: a

worker can decide to undertake a costly investment in productivity, and a firm has to decide

whether to hire the worker. The investment is only worthwhile to the worker if she is hired

by the firm, but the worker has to make the decision to invest or not before knowing if she

will be hired. The firm only wants to hire a worker if she has invested, but has to decide

on hiring the worker without knowing the worker’s choice. In our setting, summarised in

Table 1, for small enough investment costs c, there are two pure-strategy equilibria: (Invest,

Hire) and (Not Invest, Not Hire).9 The former Pareto dominates the latter; there is therefore

7There are notable econometric efforts to identify a statistical discrimination parameter in a structuralmodel (Knowles, Persico, and Todd, 2001) or in other ways (Glover, Pallais, and Pariente, 2017)). Thereare also studies that aim to control the source of discrimination in a field experiment, e.g., Agan and Starr(2018) and Ewens, Tomlin, and Wang (2014). However, broadly speaking, it is difficult to completely ruleout taste-based discrimination with field data.

8See Appendix F in Arrow’s paper; see also Coate and Loury (1993).9In principle, the presence of social preferences could alter players’ utilities such that Table 1 no longer

9

FirmHire Not Hire

WorkerInvest 1800 − c, 1600 1000 − c, 1200

Not Invest 1400, 400 1200, 1200

Table 1: The investment/hiring game, where c denotes the cost of investment.

the possibility of coordination failure, whereby workers fail to invest because they correctly

anticipate that they will not be hired.

Suppose there are two kinds of workers: GREEN workers and PURPLE workers—these

categories can stand for different genders, races, etc. If worker colour is observable, it is

possible that firms will coordinate on (Invest, Hire) with, say, GREEN workers and on

(Not Invest, Not Hire) with PURPLE workers. This situation corresponds to what we term

statistical discrimination.

The particular flavour of statistical discrimination we are interested in, based on self-

fulfilling expectations about hiring and investment, raises the question of how a society

arrives at different hiring and investment rates for GREEN and PURPLE workers. The

answer in our paper is path dependence. Our experiment starts with a “seed” stage, in which

we make investment more costly for PURPLE workers. The seed stage may then affect

beliefs in later, symmetric, rounds of play. Firms and PURPLE workers may coordinate on

the Pareto dominated equilibrium because their beliefs are anchored in a history in which

the outcome was (Not Invest, Not Hire).

The difference in investment costs at the seed stage is certainly a simplification, and is

meant to capture a combination of possible real-world differences between people of different

genders, races, and ethnicities. One possibility is that it captures literal differences in invest-

ment costs for members of disadvantaged and minority groups; for example, differences in

the cost of schooling. The difference in investment cost may also reflect other difficulties in

induces a coordination game. However, for the values of c used in the experiment, both equilibrium outcomesfeature less inequality across players’ payoffs compared to the non-equilibrium outcomes. Therefore, theequilibria of Table 1 should be unaffected under standard models of social preferences.

10

accessing the labor market, including those arising from preference-based discrimination—

historical hiring rates may have been lower for some groups.

3.2 Overview of Treatments

For the purpose of describing the experiment, we define some standard terminology. Our

experiment consists of two players playing a simultaneous-move game. Each play of the

game is a round. Experimental participants play a number of rounds in a single one-hour

long sitting: each such sitting is a session. In a session, the same group of participants

plays the game repeatedly, each participant being randomly and anonymously matched with

other participants to play the two-player game. The different sessions vary in how we set

the game parameters. A treatment is one specification of game parameters.

Our experiment is comprised of three treatments, where each treatment is run in several

sessions. In all of our treatments, each session has four stages. Each stage consists of a fixed

number of rounds. At the beginning of the session, participants are randomly assigned to

the role of either a worker or a firm. Workers are also randomly assigned a colour: GREEN

or PURPLE. Both a participant’s role, a firm or a worker, and workers’ colour are fixed

across all session rounds.

Across treatments and stages, rounds follow a fixed protocol. In each round, workers and

firms are randomly matched in pairs to play an investment/hiring game, shown in Table 1.

Each worker decides whether to invest in costly training, where c represents the cost of

investment, which is common knowledge. Each firm, knowing the colour of the worker

she is paired with, decides whether to hire the worker. Both worker and firm make their

decisions simultaneously, without observing each other’s decision. As we describe in the next

subsection, the firm’s profit from hiring a worker can depend on the stage, the worker’s colour,

and the worker’s decision to invest or not. The determination of firms’ profits varies across

our three treatments. In each round, workers and firms are also asked to report their beliefs

about the other player’s decision. For instance, a worker is asked to report her belief about

11

how likely it is that the firm chose to hire her. Similarly, a firm is asked to report her belief

about how likely it is that the worker chose to invest in training. We use the binarised scoring

rule of Hossain and Okui (2013) to incentivise belief elicitation. The binarised scoring rule is

incentive compatible even for decision makers who are not risk neutral. Before making their

decisions, all participants can observe a public history consisting of four moving averages: (1)

GREEN workers’ average investment rate, (2) PURPLE workers’ average investment rate,

(3) firms’ average hiring rate when paired with a GREEN worker, and (4) firms’ average

hiring rate when paired with a PURPLE worker. These averages are based on the decisions

of all participants across all previous rounds of the session. For maximum clarity, these

averages are reported graphically and numerically. At the end of each round, participants

observe their own and their matched participant’s decisions and payoffs. All payoffs in the

experiment are expressed in tokens, where 1 token = $0.01.10

At the end of the experiment, participants complete two risk elicitation tasks and one

survey questionnaire. Specifically, we use the risk elicitation task from Gneezy and Potters

(1997). Each participant is given a token endowment and decides how many tokens to invest

in a risky project with a known chance of success. We use duplicate elicitations in order

to account for measurement error, see Gillen, Snowberg, and Yariv (2018). The survey

questionnaire contains basic demographic, academic, and lifestyle questions.11

3.3 Stages of the Experiment

We now describe the four stages of each session.

Stage 1: Seed Stage

In the first stage of each session (Rounds 1 - 10), GREEN and PURPLE workers face different

costs of investment. For a GREEN worker, the cost of investment is 200 tokens (c = 200

10The full set of instructions is available here: http://www.leeatyariv.com/papers/Discrimination_

Instructions.pdf11The survey details are available here: http://www.leeatyariv.com/papers/Discrimination_

Demographics.pdf

12

http://www.leeatyariv.com/papers/Discrimination_Instructions.pdf

http://www.leeatyariv.com/papers/Discrimination_Instructions.pdf

http://www.leeatyariv.com/papers/Discrimination_Demographics.pdf

http://www.leeatyariv.com/papers/Discrimination_Demographics.pdf

in Table 1). For a PURPLE worker, the cost of investment is 600 tokens (c = 600). These

parameters generate two different games depending on the particular worker-firm matching.

Notably, PURPLE workers have a dominant strategy of not investing. When a firm is paired

with a PURPLE worker, iterated elimination of strictly dominated strategies yields (Not

Invest, Not Hire) as the unique outcome; (Not Invest, Not Hire) is therefore the unique Nash

equilibrium of the game. When a firm is paired with a GREEN worker, however, the strategic

environment is a coordination game with two pure-strategy Nash equilibria: (Invest, Hire)

and (Not Invest, Not Hire). The (Invest, Hire) equilibrium is Pareto-dominant. For each

participant, playing their component of the Pareto-dominant equilibrium is a best response

if the other participant is playing their component of the equilibrium with a probability of

at least 23. Stage 1 serves to “seed” discrimination between GREEN and PURPLE workers.

Stage 2: Baseline Stage

In the second stage of each session (Rounds 11 - 20), investment costs are equalised. Both

GREEN and PURPLE workers now face an investment cost of 200 tokens (c = 200). Statis-

tical discrimination occurs if participants coordinate on the Pareto-dominant (Invest, Hire)

equilibrium when a firm plays against a GREEN worker, while participants coordinate on

the Pareto-dominated (Not Invest, Not Hire) equilibrium when a firm plays against a PUR-

PLE worker.12 The purpose of Stage 2 is twofold. The first is to test whether statistical

discrimination emerges in the lab, once “seeded” by Stage 1. The second is to assess the

extent to which it is alleviated over time, as the game with symmetric investment cost is

played repeatedly.

12We focus here on the two pure-strategy equilibria, though in principle, we could consider discriminatoryoutcomes as ones in which GREEN and PURPLE workers engage in different equilibrium behaviour moregenerally. As will be seen, individuals do not appear to play the mixed-strategy equilibrium in our data.

13

Stage 3: Introducing Affirmative Action

In the third stage of each session, we maintain equal investment costs for both colours, but

we implement an affirmative-action policy to incentivise the hiring of PURPLE workers. The

policy takes the form of a subsidy s for any firm that chooses to hire a PURPLE worker,

regardless of whether or not the worker invested in training. Our experimental treatments

vary the size of the subsidy and the length of this stage.

• Subsidy: For a period of 10 rounds (Rounds 21 - 30), each firm that hires a PURPLE

worker earns an additional payment of 200 tokens (s = 200). For a firm, hiring a

PURPLE worker is now a best response if the worker is investing with a probability of

at least 12.

• High Subsidy: For a period of 10 rounds (Rounds 21 - 30), each firm that hires a

PURPLE worker earns an additional payment of 900 tokens (s = 900). For a firm,

hiring a PURPLE worker is now a dominant strategy. We note that by making the

hiring of PURPLE workers a dominant strategy, the High Subsidy treatment is the

mirror image of the seed stage.

• Long Subsidy: For a period of 20 rounds (Rounds 21 - 40), each firm that hires a

PURPLE worker earns an additional payment of 200 tokens (s = 200). For a firm,

hiring a PURPLE worker is now a best response if the worker is investing with a

probability of at least 12.

Stage 4: Removing Affirmative Action

In the fourth stage of each session (Subsidy and High Subsidy: Rounds 31 - 40, Long Subsidy:

Rounds 41 - 50), the subsidy is removed. The parameters of Stage 4 are identical to those

of Stage 2.

14

Subsidy High Subsidy Long Subsidy

Length of Experiment 40 rounds 40 rounds 50 roundsLength of Stage 3 10 rounds 10 rounds 20 rounds

Subsidy for Hiring GREEN (Stage 3) s = 0 s = 0 s = 0Beliefs for Hiring GREEN (Stage 3) pInvest ≥ 2

3pInvest ≥ 2

3pInvest ≥ 2

3

Subsidy for Hiring PURPLE (Stage 3) s = 200 s = 900 s = 200Beliefs for Hiring PURPLE (Stage 3) pInvest ≥ 1

2pInvest ≥ 0 pInvest ≥ 1

2

Number of Sessions 5 5 5Number of Participants 88 84 96

Table 2: A summary of our experimental treatments.

3.4 Implementation

All experimental sessions were run at the Experimental Social Science Laboratory (ESSL) at

UC Irvine. A total of 268 participants participated in 15 sessions. A summary of the treat-

ments and corresponding sessions appears in Table 2. Each session lasted approximately one

hour. Each participant’s earnings were the sum of a $7 show-up payment, their payoff from

one randomly selected experimental round, and their payoff from one randomly selected risk-

elicitation task. Average participant earnings were $24.46 (including the show-up payment).

The experiment was programmed and conducted using the oTree software (Chen, Schonger,

and Wickens, 2016).

4 Experimental Outcomes

We describe our results using the entire set of data. In the Online Appendix, we replicate

the analysis using the last five rounds of each stage, in order to account for potential learning

effects. The analysis using the last five rounds yields identical conclusions. Unless otherwise

stated, statistical significance is assessed using probit regressions of the relevant outcome

variable (i.e., investment or hiring) on a dummy variable for worker colour. Standard errors

are clustered at the individual level, which accounts for dependencies across observations

that arise if some subjects in firm (worker) roles are prone to hiring (investing) at higher

15

Seed StageTreatment Investment Hiring

GREEN PURPLE GREEN PURPLE

Subsidy 0.90 >∗∗∗ 0.07 0.91 >∗∗∗ 0.14High Subsidy 0.92 >∗∗∗ 0.14 0.90 >∗∗∗ 0.17Long Subsidy 0.88 >∗∗∗ 0.05 0.84 >∗∗∗ 0.10

Table 3: Investment/hiring decisions in the seed stage (unequal investment costs)Significance levels are indicated as follows: *** p < 0.01

rates than other subjects. More conservative tests, with clustering at the session level, are

included in the Online Appendix. These tests yield qualitatively similar conclusions. We also

show in the Online Appendix that responses of workers and firms to changing parameters

are simultaneous and neither appears to precede the other.13

4.1 Outcomes Across Stages

4.1.1 Inducing Statistical Discrimination

We first look at investment and hiring decisions in Stage 1, the seeding stage, when GREEN

and PURPLE workers face different costs of investment. Table 3 shows average invest-

ment and hiring rates by worker colour. Indeed, GREEN workers invest—and are hired—at

significantly higher rates than PURPLE workers in all three treatments.

In Stage 2, the baseline stage, we equalise investment costs across workers. Table 4 shows

average investment and hiring rates by worker colour. Differences in investment and hiring

across worker colours persist, though are less stark. In all cases but one, these differences

are statistically significant at conventional levels.14 These baseline differences in investment

and hiring rates for workers of different colours reflect statistical discrimination.

We now look more closely at workers’ investment decisions in Stages 1 and 2. Recall that

13The Online Appendix is available here: http://www.leeatyariv.com/papers/

AffirmativeActionAppendix.pdf14The sole exception is workers’ investment decisions in the Long Subsidy treatment, which follow the

same pattern, but are not significantly different across colours at the 10% confidence level.

16

http://www.leeatyariv.com/papers/AffirmativeActionAppendix.pdf

http://www.leeatyariv.com/papers/AffirmativeActionAppendix.pdf

Baseline StageTreatment Investment Hiring


Subsidy 0.86 >∗∗∗ 0.50 0.89 >∗∗∗ 0.52High Subsidy 0.89 >∗∗∗ 0.58 0.90 >∗∗∗ 0.54Long Subsidy 0.83 > 0.75 0.83 >∗∗∗ 0.63

Table 4: Investment/hiring decisions in the baseline stage (equal investment costs)Significance levels are indicated as follows: *** p < 0.01

PURPLE workers have a dominant strategy of not investing in Stage 1 of the experiment.

Pooling all three treatments, we find that 60% (40/67) of PURPLE workers consistently play

their dominant strategy while 90% (60/67) of PURPLE workers deviate from their dominant

strategy no more than twice over the 10 rounds of play. At the same time, 66% (44/67) of

GREEN workers consistently invest in all Stage 1 rounds. When the investment costs are

equalised in Stage 2, only 27% (18/67) of PURPLE workers invest in all rounds while 75%

(50/67) of GREEN workers invest in all rounds. However, we also observe that few PURPLE

workers continue to play their component of the Pareto-dominated equilibrium “seeded” in

Stage 1: only 12% (8/67) of PURPLE workers consistently fail to invest in all Stage 2 rounds.

The empirical cumulative distribution functions (CDFs) of participant-level investment

rates are shown in Figure 2 (panels a - f).15 Unsurprisingly, we observe sharp differences

in Stage 1 behaviour. In all cases except one, it is clear that the empirical distribution for

GREEN workers first-order stochastically dominates the empirical distribution for PURPLE

workers. In all cases except one, we can also reject the null hypothesis that the average in-

vestment rates for GREEN and PURPLE workers come from the same underlying theoretical

distribution (assessed with a Kolmogorov-Smirnov test yielding p < 0.001).16

We conduct a similar exercise with respect to firms’ hiring decisions.17 The empirical

15An independent observation corresponds to a worker’s average investment rate across all rounds of thestage.

16As before, the sole exception is workers’ investment decisions in Stage 2 of the Long Subsidy treatment,where the Kolmogorov-Smirnov test yields p = 0.183.

17Since firms interact with both worker types in a given stage, we calculate a pair of observations foreach firm: their average hiring rate when facing GREEN workers and their average hiring rate when facing

17

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

Figure 2: Empirical CDFs of participant-level behaviour before affirmative action

18

CDFs of participant-level hiring rates are also shown in Figure 2 (panels g - l). Consistent

with our observations pertaining to workers’ behaviour, the empirical distribution for hiring

GREEN workers first-order stochastically dominates the empirical distribution for hiring

PURPLE workers in all cases. We can also reject the null hypothesis that the average

hiring rates for GREEN and PURPLE workers come from the same theoretical distribution

(assessed with a Kolmogorov-Smirnov test yielding p < 0.001 in all cases).

Our analysis throughout utilises our full experimental data. Given that discriminatory

behaviour is less pronounced in the baseline stage of the Long Subsidy treatment, especially

when considering workers’ behaviour, it is natural to worry that some of our conclusions

are driven by limited inducement of discrimination in that treatment. We note, however,

that the focus of most of our analysis is on the effects of affirmative action and its removal

relative to the baseline stage. In fact, even when we eliminate the 3 sessions exhibiting the

least difference in hiring rates across GREEN and PURPLE workers in the baseline stage

(one of which belongs to the High Subsidy treatment and two of which belong to the Long

Subsidy treatment), the results reported here remain qualitatively unchanged.

Looking at aggregate investment and hiring rates in Stage 2 could lead to the conclusion

that workers and firms are coordinating on the mixed-strategy equilibrium. However, Fig-

ure 2 casts doubt on this interpretation. In particular, at the individual level, both PURPLE

workers and firms paired with them do not appear to be concentrating their strategies around

those prescribed by the mixed-strategy equilibrium (i.e., invest and hire with 23

probability).

4.1.2 Introducing Affirmative Action

In Stage 3 of each experimental treatment, we introduce an affirmative-action policy in which

each firm who hires a PURPLE worker is paid an additional subsidy. The size of the subsidy

and its duration vary across our three treatments.

Table 5 shows average investment and hiring rates by worker colour. Compared to the

PURPLE workers.

19

Introducing AATreatment Investment Hiring


Subsidy 0.76 > 0.65 0.73 > 0.70High Subsidy 0.78 > 0.69 0.72 <∗ 0.86Long Subsidy 0.74 < 0.88 0.69 <∗∗∗ 0.85

Table 5: Investment/hiring decisions during affirmative actionSignificance levels are indicated as follows: *** p < 0.01, * p < 0.10

rates in Table 4, we see a notable decrease in discriminatory outcomes. In particular, there

are no longer significant differences across worker colour when it comes to workers’ invest-

ment decisions. That being said, the average investment rates of PURPLE workers still

lag behind those of GREEN workers in both the Subsidy and High Subsidy treatments

(where affirmative action lasts only 10 rounds). In other words, PURPLE workers do not

fully internalise firms’ responses to subsidies. It may seem odd that this occurs even in the

High Subsidy treatment, when firms have a dominant strategy of hiring PURPLE workers

and hire PURPLE workers at even greater rates than those pertaining to GREEN work-

ers. However, investment by PURPLE workers in this treatment requires “second-order”

rationality—PURPLE workers have to be rational and to also believe that firms are ratio-

nal. The investment rate in our data (69%) is comparable to the estimate of second-order

rationality (71%) found in Kneeland (2015).

The three affirmative-action policies we test are also effective in manipulating firms’ hiring

behaviour. In the Subsidy treatment (10 rounds, s = 200), firms no longer hire GREEN and

PURPLE workers at significantly different rates. However, intensifying the affirmative-action

policy by either increasing the size of the subsidy (from s = 200 to s = 900) or increasing the

length of the subsidy (from 10 rounds to 20 rounds) causes firms to favour PURPLE workers

in their hiring decisions. The impact of the subsidy increase is only modestly significant,

while the impact of lengthening the subsidy is highly significant.

It is interesting to note that investment and hiring rates of PURPLE workers in the

20

(a) (b)

(c) (d)

(e) (f)

Figure 3: Empirical CDFs of participant-level behaviour during affirmative action

21

Removing AATreatment Investment Hiring


Subsidy 0.80 >∗∗∗ 0.48 0.72 >∗∗∗ 0.42High Subsidy 0.83 >∗∗ 0.59 0.78 >∗∗∗ 0.52Long Subsidy 0.80 > 0.67 0.71 > 0.63

Table 6: Investment/hiring decisions after affirmative actionSignificance levels are indicated as follows: *** p < 0.01, ** p < 0.05

affirmative-action stage of the Long Subsidy treatment substantially exceed those observed

in the Subsidy treatment, especially given that the first 10 rounds of the affirmative-action

stage are identical in both treatments. This hints at an insight we will return to in Section 5.

Knowing that the subsidy will remain in place for a long duration seems to affect behaviour

even in the initial rounds following the introduction of affirmative action.

The individual-level data further confirm that affirmative action is largely successful

in reversing the previously-observed differences across worker colours. Figure 3 shows the

empirical CDFs of participant-level investment and hiring rates while affirmative action is

in place. For all treatments, we fail to reject the null hypothesis that GREEN and PURPLE

workers’ average investment rates come from the same distribution.18 Furthermore, for all

treatments, we fail to reject the null hypothesis that the average hiring rates of GREEN and

PURPLE workers come from the same distribution.19

4.1.3 Removing Affirmative Action

In Stage 4 of each treatment, we remove the affirmative-action subsidy. The parameters of

this stage are then identical to those of our baseline stage, Stage 2. The purpose of this

stage is to assess whether the benefits of affirmative action persist after the policy is lifted.

Table 6 depicts average investment and hiring rates by worker colour. In terms of both

18Using a Kolmogorov-Smirnov test, we have the following p-values across treatments: Subsidy, p = 0.146;High Subsidy, p = 0.057; Long Subsidy, p = 0.183.

19Using a Kolmogorov-Smirnov test, we have the following p-values across treatments: Subsidy, p = 0.743;High Subsidy, p = 0.347; Long Subsidy, p = 0.187.

22

investment and hiring decisions, we observe a surprising reversion to pre-affirmative action

patterns of behaviour. In all three treatments, GREEN workers invest at higher rates than

PURPLE workers. However, the duration of the affirmative-action policy seems to matter:

these differences are statistically significant in the Subsidy and High Subsidy treatments but

not in the Long Subsidy treatment.

Firms’ hiring decisions exhibit a similar pattern. In the Subsidy and High Subsidy

treatments, firms hire GREEN workers at higher rates than PURPLE workers. Moreover,

both of these differences are statistically significant. In fact, the shorter affirmative-action

policies end up backfiring since the hiring rates of PURPLE workers are even lower in these

two treatments than in the baseline stage.

With a longer period of affirmative action in the Long Subsidy treatment, we once again

see that the deleterious effects of removing the subsidy are less severe. After the affirmative-

action policy is lifted, firms’ hiring rates of GREEN and PURPLE workers appear closer

and we fail to reject the null hypothesis that both worker types are hired at the same

rate. Combined, this evidence suggests that a longer duration of affirmative action can have

beneficial and lasting effects that extend beyond the life of the policy itself.

Figure 4 displays the empirical CDFs of participant-level behaviour, both investment

and hiring, after the affirmative-action policy is lifted. In all cases except one, the empiri-

cal distribution for GREEN workers first-order stochastically dominates the corresponding

empirical distribution for PURPLE workers.20 This provides further evidence that discrim-

ination in favour of GREEN workers persists in our experimental labor markets—even long

after the explicit advantage of GREEN workers has been eliminated. With regard to in-

vestment decisions, we can reject the null hypothesis that GREEN and PURPLE workers’

average investment rates come from the same distribution in the Subsidy treatment, but

not in the High Subsidy and Long Subsidy treatments.21 With regard to hiring decisions,

20The sole exception is firms’ hiring decisions in the Long Subsidy treatment.21Specifically, using the Kolmogorov-Smirnov test, we get the following p-values across treatments: Sub-

sidy, p = 0.004; High Subsidy, p = 0.129; Long Subsidy, p = 0.342.

23

(a) (b)

(c) (d)

(e) (f)

Figure 4: Empirical CDFs of participant-level behaviour after affirmative action

24

we can reject the null hypothesis that firms’ average hiring rates for GREEN and PURPLE

workers come from the same distribution in the Subsidy and High Subsidy treatments.22

These observations further testify that a longer duration of affirmative action can mitigate

the reversal of the policy gains when the policy is eventually lifted.23

We note that there is a striking asymmetry between the effects of the seeding and affir-

mative action stages. Seeding creates a long-lasting difference in how GREEN and PURPLE

workers behave, and how firms treat them. The affirmative-action policy is similar in that it

modifies firms’ payoffs in order to undo statistical discrimination by favouring the hiring of

PURPLE workers. However, this policy is nowhere close to being as effective as the initial

seeding. This observation is particularly interesting with respect to our High Subsidy treat-

ment, which effectively mirrors the seeding stage—it lasts for an identical period of time and

involves a dominant strategy for firms of hiring PURPLE workers. Nonetheless, when the

High Subsidy affirmative-action policy is lifted, discriminatory outcomes reappear.

4.2 Behaviour within Colour across Stages

Since the primary focus of this study is on discrimination and the effectiveness of affirmative

action policies in combatting it, our data analysis is based on differences across colour within

stages. As outlined earlier, we find that all three affirmative action policies are successful

in significantly and meaningfully reducing the disparities between GREEN and PURPLE

workers when the policies are in place.

At the same time, there are clear patterns that emerge within colour across stages. In

Tables 7- 10, we reproduce the earlier average investment/hiring rates and conduct statistical

tests to measure whether within-colour behaviour changes across the different stages of the

experiment.24 The trends for PURPLE workers are consistent with our intuition: introducing

22Using the Kolmogorov-Smirnov test ,we get the following p-values across treatments: Subsidy, p = 0.001;High Subsidy, p = 0.005; Long Subsidy, p = 0.793.

23While we focus on statistical discrimination alone, we suspect that the presence of taste-based discrimi-nation in environments such as ours would only exacerbate the outcomes we report.

24Statistical significance across two stages is assessed using probit regressions of the relevant outcome

25

affirmative action increases both investment and hiring rates, while removing affirmative

action undoes those gains. For the two shorter affirmative action policies, we actually find

that the hiring rate of PURPLE workers is lower post-intervention (Stage 4) than pre-

intervention (Stage 2), although neither of these two decreases is statistically significant.

The trends for GREEN workers are more surprising. We observe decreases in both in-

vestment and hiring rates when the affirmative action policy is put in place. Furthermore,

the drop in GREEN hiring is significant at the 1% level and fails to rebound when the affir-

mative action policy is removed. Indeed, the hiring rate of GREEN workers is significantly

lower post-intervention (Stage 4) than pre-intervention (Stage 2) in all three treatments.25

This result is puzzling. In our experiment, firms are paired with a single worker colour

in each round and there are no hiring constraints faced by firms across rounds. Thus, an

affirmative action policy that favours PURPLE workers should not affect any interactions

involving GREEN workers.

We provide one potential explanation for this puzzle: introducing affirmative action for a

disadvantaged group might demoralise or otherwise breed the resentment of the advantaged

group. If this is the case, and firms correctly internalise this logic, then the prediction is

that both GREEN investment and hiring rates should fall. We note, however, that this

explanation falls outside of the scope of both our theoretical model and our experimental

design. As such, it should be taken with a grain of salt.

variable (i.e., investment or hiring) on a dummy variable for one of the two stages. Standard errors areclustered at the individual level.

25This difference is significant at the 1% level in the Subsidy and High Subsidy treatments, and at the 5%level in the Long Subsidy treatment.

26

GREEN Investment

Treatment Seed Baseline Introducing AA Removing AA

Subsidy 0.90 > 0.86 >∗∗ 0.76 <∗ 0.80

High Subsidy 0.92 > 0.89 >∗ 0.78 < 0.83

Long Subsidy 0.88 >∗ 0.83 >∗ 0.74 <∗ 0.80

Table 7: Investment decisions of GREEN workers (across all stages)Significance levels are indicated as follows: ** p < 0.05, * p < 0.10

GREEN Hiring


Subsidy 0.91 > 0.89 >∗∗∗ 0.73 > 0.72

High Subsidy 0.90 = 0.90 >∗∗∗ 0.72 < 0.78

Long Subsidy 0.84 > 0.83 >∗∗∗ 0.69 < 0.71

Table 8: Hiring decisions involving GREEN workers (across all stages)Significance levels are indicated as follows: *** p < 0.01

PURPLE Investment


Subsidy 0.07 <∗∗∗ 0.50 <∗ 0.65 >∗∗ 0.48

High Subsidy 0.14 <∗∗∗ 0.58 < 0.69 > 0.59

Long Subsidy 0.05 <∗∗∗ 0.75 <∗ 0.88 >∗∗∗ 0.67

Table 9: Investment decisions of PURPLE workers (across all stages)Significance levels are indicated as follows: *** p < 0.01, ** p < 0.05, * p < 0.10

27

PURPLE Hiring


Subsidy 0.14 <∗∗∗ 0.52 <∗∗∗ 0.70 >∗∗∗ 0.42

High Subsidy 0.17 <∗∗∗ 0.54 <∗∗∗ 0.86 >∗∗∗ 0.52

Long Subsidy 0.10 <∗∗∗ 0.63 <∗∗∗ 0.85 >∗∗∗ 0.63

Table 10: Hiring decisions involving PURPLE workers (across all stages)Significance levels are indicated as follows: *** p < 0.01

4.3 Choice from a Menu

In our experiments, each firm is randomly paired with a particular worker and faces a binary

hiring decision. In a labor market setting, however, firms are typically confronted with the

choice of which worker to hire from a menu of workers. The efficacy of an affirmative-action

policy would then be measured by its ability to nudge firms to hire certain types of workers

from a menu containing their favoured workers. Our data allow us to deduce expected choices

from such menus of workers with and without affirmative-action policies in place. That is,

we can use our data to deduce how often firms would hire a PURPLE worker when given

the choice of hiring either type of worker.

In each round of the experiment, firms are asked to report their belief about the likelihood

that the workers they are paired with chose to invest in training. Similarly, workers are asked

to report their belief about the likelihood that the firms they are paired with chose to hire

them.26 Using these belief elicitations, we first calculate each firm’s average reported beliefs

for GREEN and PURPLE workers’ investment rates in each stage of the experiment. Using

these, we then calculate each firm’s expected payoffs from hiring GREEN and PURPLE

workers in each stage of the experiment. In the following section, we show that firms best-

respond to their reported beliefs. We therefore assume that, when faced with a menu, a

26As mentioned, we use the binarised scoring rule of Hossain and Okui (2013) to incentivise belief elicita-tion. This rule is incentive-compatible even for decision-makers who are not risk-neutral.

28

Seed Stage Baseline Stage Introducing AA Removing AA

Subsidy 0.00 0.05 0.48 0.07High Subsidy 0.05 0.07 1.00 0.21Long Subsidy 0.06 0.17 0.90 0.40

Table 11: Fraction of firms hiring a PURPLE worker over a GREEN worker

firm would hire a PURPLE worker only if her expected payoff of hiring a PURPLE worker

is strictly greater than her expected payoff of hiring a GREEN worker. Table 11 shows the

fraction of firms hiring a PURPLE worker over a GREEN worker under these assumptions

(using the shorthand AA for affirmative action).

Consistent with our previous findings, we see that PURPLE workers would be hired at

a significantly higher rate when affirmative action is introduced (two-sided t-test: p < 0.001

in all three treatments). However, when affirmative action is removed, the hiring rate for

PURPLE workers would decline substantially. For the Subsidy treatment, in fact, the hiring

rate for PURPLE workers after the policy intervention would not be significantly different

than prior to the policy intervention (two-sided t-test: p = 0.65). For the High Subsidy and

Long Subsidy treatments, we find that there would be modestly significant differences in the

hiring rates of PURPLE workers before and after the policy interventions (two-sided t-test:

p = 0.06 for High Subsidy, p = 0.01 for Long Subsidy). Again, this underscores the point

that stronger affirmative-action policies can have longer-lasting positive effects.

To conclude, by extrapolating our belief-elicitation data, we derive predictions for a

richer market environment that echo our main findings. Statistically discriminated-against

workers, who compete against more initially “desirable” workers, benefit from affirmative-

action policies, but often only while those policies are still in place.

29

Seed StageSubsidy High Subsidy Long Subsidy

GREEN workers 0.85/0.84 0.71/0.85 0.78/0.81PURPLE workers 0.93/0.93 0.86/0.86 0.95/0.95Firms paired with GREEN 0.80/0.80 0.78/0.79 0.74/0.78Firms paired with PURPLE 0.90/0.86 0.85/0.83 0.90/0.90

Baseline StageSubsidy High Subsidy Long Subsidy


Introducing Affirmative ActionSubsidy High Subsidy Long Subsidy


Removing Affirmative ActionSubsidy High Subsidy Long Subsidy


Table 12: Fraction of best-responses to reported beliefs/public histories

30

5 Beliefs as a Channel for Persistence

So far, we focused on the binary outcomes of our experimental interactions (invest or not

for workers; hire or not for firms). We now investigate the evolution of participants’ beliefs

throughout our experiment. As we will see, beliefs are sticky: while agents respond to the

pecuniary incentives that subsidies introduce, their beliefs are not altered dramatically.

We first inspect the linkages between beliefs and actions. We consider the question of

whether participants are playing best-response strategies, both with respect to their reported

beliefs and with respect to the public history of play. Table 12 shows the breakdown of best-

response rates by participant role/colour, treatment, and stage. As can be seen, participants’

actions are largely optimal given their reported beliefs. In aggregate, 85% (7,534/8,880) of

participants’ actions are a best response to their reported beliefs.27 Participants best respond

to the public history at far lower rates, standing at 73% (6,483/8,880). This is reasonable—

since the public history includes the results from all previous rounds and does not reset

between stages, less sensitivity to the public history implies sensitivity to the changing

parameters/incentives of the experiment.

One might wonder whether participants “develop” taste-based discrimination throughout

our experiment. The patterns of best-responses suggest they do not. Indeed, firms that best

respond to their beliefs hire GREEN workers at significantly greater rates than PURPLE

workers. However, firms that do not best respond to their beliefs, whom one might suspect

to have developed discriminatory attitudes that go beyond the statistical, actually hire PUR-

PLE workers at comparable or higher rates (albeit, insignificantly so). Furthermore, firms’

beliefs regarding their paired workers’ investment conditional on hiring are less optimistic

for PURPLE workers. That is, firms do not appear to require a higher threshold of belief

for PURPLE workers.

While participants’ actions are consistent with their beliefs, actions are far coarser. The

27This level is consistent, if somewhat higher, than other reported statistics of best responses, see e.g.Rey-Biel (2009) and references therein.

31

evolution of beliefs throughout our sessions thus provides insight into the action choices we

observe. Figure 5 illustrates workers’ average beliefs across rounds and Figure 6 illustrates

firms’ average beliefs across rounds, along with the average public history that was visible

to participants on the experimental interface.

Reported beliefs roughly reflect trends of the public history, but differ in magnitudes

and slopes. They are slightly less optimistic for GREEN workers and substantially more

optimistic for PURPLE workers. In particular, participants do not simply mirror the public

history when reporting beliefs.

Importantly, while we see a jump in beliefs pertaining to PURPLE workers’ investment

after the seeding stage, beliefs remain fairly flat afterwards, with only slight increases during

the affirmative-action phase, which flattens out during the affirmative-action phase of our

Long Subsidy treatment. The level of beliefs is such that, absent subsidies, the decision to

hire is only marginally optimal in some cases, whereas it is clearly optimal when affirmative-

action incentives are in place.28

In contrast, beliefs regarding GREEN workers are slightly below those suggested by their

actual investment rates. Naturally, one needs to take with care any impression that beliefs

are pessimistic. Indeed, experimental investment rates by GREEN workers are rather high.

Therefore, any perturbations of those statistical rates that generate beliefs would generally

shift average assessments down. Regardless, beliefs are sufficiently high as to guarantee

hiring throughout the different experimental stages.

In the Online Appendix, we also show that participants generally hold well-calibrated

beliefs, tracking rather closely observed behaviour. Nonetheless, in line with our description

above, when focusing on PURPLE workers and the firms they are paired with, we see

excessive optimism in the first, seeding stage. Firms and workers are overly pessimistic

28This could be an indication that participants are simply coordinating on the mixed-strategy equilibriumof the game in the baseline and final stages, which would be consistent with the reported beliefs. At theindividual level, however, behaviour in these stages is inconsistent with that equilibrium (see Section 4.1).

32

Figure 5: Workers’ beliefs and firm hiring history (solid black lines illustrate threshold beliefsfor investment to be optimal)

33

Figure 6: Firms’ beliefs and worker investment history (solid black lines illustrate thresholdbeliefs for hiring to be optimal)

34

when affirmative action is introduced, and then overly optimistic when it is lifted.

In order to quantify different stages’ impacts on beliefs as well as summarise the results

of the paper, we estimate the following OLS regressions separately for each treatment. Since

we are primarily interested in the impact of affirmative action and its removal, we restrict

our analysis to PURPLE workers and firms interacting with PURPLE workers in Stages 2 -

4 of the experiment.

WorkerBeliefit = βWB0 + βWB

1 ∗ IntroducingAAt + βWB2 ∗RemovingAAt + εit,

Investit = βI0 + βI

1 ∗ IntroducingAAt + βI2 ∗RemovingAAt + εit,

F irmBeliefit = βFB0 + βFB

1 ∗ IntroducingAAt + βFB2 ∗RemovingAAt + εit,

Hireit = βH0 + βH

1 ∗ IntroducingAAt + βH2 ∗RemovingAAt + εit,

where WorkerBeliefit is PURPLE worker i’s reported belief (between 0 and 1) about the

likelihood that its paired firm in round t chose to hire, Investit is a dummy variable that

equals 1 if PURPLE worker i invests in training in round t, FirmBeliefit is firm i’s reported

belief (between 0 and 1) about the likelihood that its paired PURPLE worker in round t

chooses to invest in training, Hireit is a dummy variable that equals 1 if firm i hires a

PURPLE worker in round t, IntroducingAAt is a dummy variable that equals 1 if round t is

in Stage 3 of the experiment (when affirmative action is introduced), and RemovingAAt is

a dummy variable that equals 1 if round t is in Stage 4 of the experiment (when affirmative

action is removed). Last, εit is an error term, which we cluster by participant.

The regression results are shown in Tables 13-16. The first three columns correspond

to our three treatments. The fourth treatment splits the first 10 and last 10 periods of the

affirmative-action stage in the Long Subsidy treatment. The corresponding regression allows

us to infer whether the length of the subsidy is internalised by participants early on. Indeed,

absent forward-looking behaviour, we would expect that the first 10 rounds of the affirmative-

35

action stage in the Long Subsidy treatment are equivalent to the full affirmative-action stage

in the Subsidy treatment.

Echoing our previous observations, affirmative action is effective in altering both firms’

beliefs and hiring decisions while the policy is in place. For each treatment, the coefficient

estimates β̂H1 and β̂FB

1 are positive and statistically significant. For a given treatment, we

can then compare the magnitudes of β̂H1 and β̂FB

1 to capture the relative effectiveness of

the affirmative-action policy in changing firms’ actions and beliefs. Across all treatments,

we see that β̂H1 > β̂FB

1 . That is, firms’ beliefs are less responsive to the policy intervention

than firms’ hiring decisions. The opposite is true of workers. Workers’ decision to invest

depends on whether they expect firms to hire with probability greater than 2/3, a threshold

that does not change with the AA policy, as it does for firms. Workers appear to internalise

firms’ pecuniary incentives to hire when affirmative action is in place, so that their beliefs

become significantly more optimistic. However, the change in beliefs does not always justify

a change in actions, and hence workers’ investment exhibits a weaker response to affirmative

action and its removal.

The coefficient estimates β̂FB2 and β̂H

2 measure the extent to which affirmative action’s

benefits, in terms of the market’s response to workers, persist even after the policy is lifted.

In each treatment, we find no statistically significant difference in the hiring of PURPLE

workers between the affirmative-action stage and after affirmative action is lifted. However,

β̂H2 > 0 only for the Long Subsidy treatment, albeit insignificantly so. In a similar vein,

looking at firms’ beliefs about PURPLE workers, the coefficient estimate β̂FB2 is positive

and, here, statistically significant only for the Long Subsidy treatment. Analogously, while

workers are more optimistic after the removal of affirmative action, they are not sufficiently

so as to induce a significant change in investment relative to the baseline stage.

The inclusion of lagged behaviours within each stage does not explain actions beyond

participants’ beliefs. In particular, we see limited evidence for reinforcement learning, or

tit-for-tat-like behaviour in which a firm encountering one worker not investing, or a worker

36

Subsidy High Subsidy Long Subsidy Long SubsidyVARIABLE: Worker Belief (1) (2) (3) (4)

Introducing AA 0.265*** 0.198*** 0.271***(0.063) (0.049) (0.057)

Removing AA 0.123** 0.079* 0.122*** 0.122***(0.057) (0.039) (0.029) (0.029)

Introducing AA (first half) 0.271***(0.054)

Introducing AA (second half) 0.272***(0.061)

Constant 0.399*** 0.555*** 0.588*** 0.588***(0.051) (0.063) (0.056) (0.057)

Observations 660 630 960 960Number of clusters 22 21 24 24

Table 13: Results from OLS regressions. Standard errors are shown in parentheses and areclustered at the individual level. Significance levels are indicated as follows: *** p < 0.01,** p < 0.05, * p < 0.10.

encountering one firm not hiring, affect choices dramatically. For additional robustness

results, see the Online Appendix.

The effect of affirmative action is significantly stronger in the first 10 periods of our Long

Subsidy treatment than in the phase of 10 analogous periods in our Subsidy treatment. This

suggests that participants account for the length of affirmative-action policies even when they

are first introduced. This implies that placing a longer-duration affirmative-action policy has

two advantages. A longer duration increases the effectiveness of the policy even in its early

introductory phase, in addition to enhancing its long-run effects after its removal. Going back

to Justice Sandra Day O’Connor’s 2003 quote, it is possible that a sufficiently long phase of

affirmative action, which may or may not correspond to 25 years, would assure some erosion

of discriminatory attitudes both during and after affirmative action is in place.

In our experiments, participants also respond to two risk elicitations as well as various

37

Subsidy High Subsidy Long Subsidy Long SubsidyVARIABLE: Invest (1) (2) (3) (4)

Introducing AA 0.145 0.110 0.127*(0.086) (0.087) (0.074)

Removing AA -0.023 0.014 -0.083 -0.083(0.076) (0.078) (0.068) (0.068)

Introducing AA (first half) 0.117(0.073)

Introducing AA (second half) 0.138*(0.076)

Constant 0.500*** 0.576*** 0.754*** 0.754***(0.082) (0.077) (0.067) (0.067)



Subsidy High Subsidy Long Subsidy Long SubsidyVARIABLE: Firm Belief (1) (2) (3) (4)

Introducing AA 0.086** 0.067* 0.153***(0.041) (0.035) (0.035)

Removing AA 0.022 -0.004 0.100*** 0.100***(0.055) (0.033) (0.032) (0.032)



Constant 0.490*** 0.546*** 0.603*** 0.603***(0.044) (0.043) (0.039) (0.039)



38

Subsidy High Subsidy Long Subsidy Long SubsidyVARIABLE: Hire (1) (2) (3) (4)

Introducing AA 0.173** 0.319*** 0.225***(0.066) (0.058) (0.052)

Removing AA -0.100 -0.019 -0.004 -0.004(0.074) (0.055) (0.056) (0.056)



Constant 0.523*** 0.543*** 0.629*** 0.629***(0.059) (0.060) (0.053) (0.053)



demographic questions. Importantly, when adding these as controls, neither has a significant

effect nor do they alter the coefficients of treatment effects described above.29 The Online

Appendix contains a detailed description of this analysis. In the Online Appendix, we

also consider the possibility that firms that are more highly discriminatory in the baseline

stage respond differently to affirmative action and its removal. We classify firms into types

pertaining to their discriminatory tendencies in the baseline stage and illustrate that, indeed,

effects are more pronounced for firms that are initially more discriminatory. The qualitative

patterns, however, track those pertaining to the full set of firms.

Finally, we note that affirmative action can work through two distinct channels in our

experiment. First, affirmative action can directly manipulate firms’ underlying beliefs about

the productivity of PURPLE workers. Second, even if firms’ beliefs are unchanged, firms

can still respond positively to the pecuniary incentive associated with affirmative action.

29One exception is inclusion in a minority group, which significantly reduces hiring when affirmative actionis introduced and when it is lifted in our High Subsidy treatment. However, since this is the only significanteffect out of our five controls in the three treatments, we suspect it might be spurious.

39

To decompose these two effects, we conduct a counterfactual exercise where we investigate

firms’ optimal hiring decisions given their beliefs while the policy is in place but in the absence

of the subsidy. When affirmative action lasts for only 10 rounds, we find that firms would

hire PURPLE workers in less than half of their interactions: 42% (92/220) in the Subsidy

treatment and 47% (98/210) in the High Subsidy treatment. In the Long Subsidy treatment,

however, firms would hire PURPLE workers in 67% (320/480) of their interactions. This

underscores our earlier points about the stickiness of firms’ beliefs and the limited efficacy of

a short duration of affirmative action. Given that firms’ beliefs are not responding sufficiently

in two of our three treatments to sustain hiring in the absence of a subsidy, it should come

as no surprise that discrimination reappears when the subsidy is lifted.

6 Discussion and Conclusion

In 1961, President John F. Kennedy first utilised the term affirmative action in its contem-

porary sense in Executive Order 10925. The intention was to have government contractors

“take affirmative action to ensure that applicants are employed, and employees are treated

during employment, without regard to their race, creed, colour, or national origin.” Today,

affirmative action refers to the leading set of laws, policies, guidelines, and administrative

practices aimed at alleviating racial and gender-based discrimination. Our goal in this paper

is to use an array of lab experiments to assess the effects of affirmative-action policies in

combating statistical discrimination, while in place and after they are lifted.

Our results raise questions about the long-term effectiveness of affirmative-action policies.

To level the playing field, our findings suggest that affirmative-action policies need to be

activated for substantial periods of time. These implications relate to the empirical regularity

that affirmative-action policies tend to become entrenched, and left in place far longer than

initially intended, see Sowell (2004).

Any conclusion about the long-term effects of affirmative action should be qualified. We

40

have focused on affirmative action as an instrument for correcting statistical discrimination

in labor markets, but there are other sources of discrimination, and other environments in

which discrimination occurs. For instance, it is quite possible that exposing people to the

rich diversity of humankind may change their beliefs through various channels—role models,

exemplars, etc.—and thereby address taste-based discrimination.30 There is also a fairness

argument in favour of affirmative action—it serves as compensation for past discrimination.

Affirmative action in education does not only seek to change expectations, its objective

includes granting access to minority students who would not otherwise be able to attend good

schools or to obtain higher education (see the landmark study of Bowen and Bok (2016) for

an elaborate discussion of affirmative action in education). There are also possible dynamic

benefits from affirmative action. Even if affirmative action does not eliminate discrimination

today, it may help future generations of minorities access better opportunities. As in our

experiments, the fruits of affirmative action might simply take a long time to ripen.

30For instance, Miller (2017) illustrates some positive effects of temporary affirmative-action policies thathe explains through employers improving their hiring practices.

41

References

Agan, Amanda Y and Sonja B Starr. 2018. “Ban the Box, Criminal Records, and Statistical Discrimination:

A Field Experiment.” Quarterly Journal of Economics 133 (1):191–235.

Anderson, Donna M and Michael J Haupert. 1999. “Employment and Statistical Discrimination: A Hands-

On Experiment.” The Journal of Economics 25 (1):85–102.

Anderson, Lisa, Roland Fryer, and Charles Holt. 2006. “Discrimination: Experimental Evidence From

Psychology and Economics.” In Handbook on the Economics of Discrimination, edited by William M.

Rodgers. Edward Elgar Publishing Northampton, MA, 97–118.

Arrow, Kenneth J. 1971. “Some models of Racial Discrimination in the Labor Market.” Tech. Rep. RM-

6253-RC, RAND.

———. 1973. “The Theory of Discrimination.” In Discrimination in Labor Markets, edited by Orley

Ashenfelter and Albert Rees. Princeton University Press, 3–33.

———. 1998. “What Has Economics to Say About Racial Discrimination?” The Journal of Economic

Perspectives 12 (2):91–100.

Becker, Gary S. 1957. The Theory of Discrimination. University of Chicago Press.

Bohren, Aislinn, Alex Imas, and Michael Rosenberg. 2018. “The Dynamics of Discrimination: Theory and

Evidence.” Mimeo.

Bowen, William G and Derek Bok. 2016. The shape of the river: Long-term consequences of considering

race in college and university admissions. Princeton University Press.

Bracha, Anat, Alma Cohen, and Lynn Conell-Price. 2019. “The Heterogeneous Effect of Affirmative Action

on Performance.” Journal of Economic Behavior and Organization Forthcoming.

Brandts, Jordi and David J Cooper. 2006. “A Change Would Do You Good.... An Experimental Study on

How to Overcome Coordination Failure in Organizations.” American Economic Review 96 (3):669–693.

Chen, Daniel L, Martin Schonger, and Chris Wickens. 2016. “oTree - An Open-Source Platform for Labo-

ratory, Online, and Field Experiments.” Journal of Behavioral and Experimental Finance 9:88–97.

Coate, Stephen and Glenn C Loury. 1993. “Will Affirmative-action Policies Eliminate Negative Stereotypes?”

The American Economic Review 83 (5):1220–1240.

42

de Haan, Thomas, Theo Offerman, and Randolph Sloof. 2017. “Discrimination in the Labour Market: The

Curse of Competition between Workers.” The Economic Journal 127 (603):1433–1466.

Ewens, Michael, Bryan Tomlin, and Liang Choon Wang. 2014. “Statistical Discrimination or Prejudice? A

Large Sample Field Experiment.” Review of Economics and Statistics 96 (1):119–134.

Feltovich, Nick, Lata Gangadharan, and Michael P Kidd. 2013. “Implementation and Removal of an

Affirmative-Action Quota: The Impact on Task Assignment and Workers’ Skill Acquisition.” Canadian

Public Policy 39 (Supplement 1):S123–S140.

Fryer, Roland G, Jacob K Goeree, and Charles A Holt. 2005. “Experience-based Discrimination: Classroom

Games.” The Journal of Economic Education 36 (2):160–170.

Gillen, Ben, Erik Snowberg, and Leeat Yariv. 2018. “Experimenting with Measurement Error: Techniques

With Applications to The Caltech Cohort Study.” Journal of Political Economy Forthcoming.

Glover, Dylan, Amanda Pallais, and William Pariente. 2017. “Discrimination as a Self-Fulfilling Prophecy:

Evidence from French Grocery Stores.” Quarterly Journal of Economics 132 (3):1219–1260.

Gneezy, Uri and Jan Potters. 1997. “An Experiment on Risk Taking and Evaluation Periods.” Quarterly

Journal of Economics 112 (2):631–645.

Hossain, Tanjim and Ryo Okui. 2013. “The Binarized Scoring Rule.” Review of Economic Studies 80 (3):984–

1001.

Kidd, Michael P, Paul S Carlin, and Jonathan Pot. 2008. “Experimenting with Affirmative Action: The

Coate and Loury Model.” Economic Record 84 (266):322–337.

Kneeland, Terri. 2015. “Identifying Higher-Order Rationality.” Econometrica 83 (5):2065–2079.

Knowles, John, Nicola Persico, and Petra Todd. 2001. “Racial Bias in Motor Vehicle Searches: Theory and

Evidence.” Journal of Political Economy 109 (1):203–229.

Krueger, Alan, Jesse Rothstein, and Sarah Turner. 2006. “Race, Income, and College in 25 Years: Evaluating

Justice O’Connor’s Conjecture.” American Law and Economics Review 8 (2):282–311.

Miller, Conrad. 2017. “The Persistent Effect of Temporary Affirmative Action.” American Economic Journal:

Applied Economics 9 (3):152–90.

43

Niederle, Muriel, Carmit Segal, and Lise Vesterlund. 2013. “How Costly is Diversity? Affirmative Action in

Light of Gender Differences in Competitiveness.” Management Science 59 (1):1–16.

Phelps, Edmund S. 1972a. “The Statistical Theory of Racism and Sexism.” The American Economic Review

62 (4):659–661.

Phelps, Edmund S. 1972b. “The Statistical Theory of Racism and Sexism.” American Economic Review

62 (4):659–661.

Rey-Biel, Pedro. 2009. “Equilibrium Play and Best Response to (Stated) Beliefs in Normal Form Games.”

Games and Economic Behavior 65 (2):572–585.

Romero, Julian. 2015. “The Effect of Hysteresis on Equilibrium Selection in Coordination Games.” Journal

of Economic Behavior & Organization 111:88–105.

Sander, Richard H. 2004. “A Systematic Analysis of Affirmative Action in Law Schools.” Stanford Law

Review 57:367–483.

Sander, Richard H. and Stuart Taylor. 2012. Mismatch: How Affirmative Action Hurts Students It’s Intended

to Help, and Why Universities Won’t Admit It. Basic Books.

Sowell, Thomas. 2004. Affirmative Action Around the World: An Empirical Study. Yale University Press.

44

Statistical Discrimination and A rmative Action in …fede/wp/discrimination.pdfStatistical...

Documents

Transcript of Statistical Discrimination and A rmative Action in …fede/wp/discrimination.pdfStatistical...